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Simplificación de expresiones/ Descomposición en fracciones simples/ pi*(2*cos(2x-1))/((tg(pi*x)^2)*(cos(pi*x)^2))

¿Cómo vas a descomponer esta pi*(2*cos(2x-1))/((tg(pi*x)^2)*(cos(pi*x)^2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  pi*2*cos(2*x - 1)  
---------------------
   2          2      
tan (pi*x)*cos (pi*x)
π2cos⁡(2x−1)cos⁡2(πx)tan⁡2(πx)\frac{\pi 2 \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
(pi*(2*cos(2*x - 1)))/((tan(pi*x)^2*cos(pi*x)^2))
Simplificación general [src] 
4*pi*cos(-1 + 2*x)
------------------
 1 - cos(2*pi*x)
4πcos⁡(2x−1)1−cos⁡(2πx)\frac{4 \pi \cos{\left(2 x - 1 \right)}}{1 - \cos{\left(2 \pi x \right)}} 
4*pi*cos(-1 + 2*x)/(1 - cos(2*pi*x))
Respuesta numérica [src] 
6.28318530717959*cos(2*x - 1)/(cos(pi*x)^2*tan(pi*x)^2)
6.28318530717959*cos(2*x - 1)/(cos(pi*x)^2*tan(pi*x)^2)
Denominador común [src] 
  2*pi*cos(-1 + 2*x) 
---------------------
   2          2      
cos (pi*x)*tan (pi*x)
2πcos⁡(2x−1)cos⁡2(πx)tan⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
2*pi*cos(-1 + 2*x)/(cos(pi*x)^2*tan(pi*x)^2)
Combinatoria [src] 
  2*pi*cos(-1 + 2*x) 
---------------------
   2          2      
cos (pi*x)*tan (pi*x)
2πcos⁡(2x−1)cos⁡2(πx)tan⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
2*pi*cos(-1 + 2*x)/(cos(pi*x)^2*tan(pi*x)^2)
Potencias [src] 
  2*pi*cos(-1 + 2*x) 
---------------------
   2          2      
cos (pi*x)*tan (pi*x)
2πcos⁡(2x−1)cos⁡2(πx)tan⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
                        2                                
    / pi*I*x    -pi*I*x\  / I*(1 - 2*x)    I*(-1 + 2*x)\ 
-pi*\e       + e       / *\e            + e            / 
---------------------------------------------------------
                          2                              
      / pi*I*x    -pi*I*x\                        2      
      |e         e       |  /   pi*I*x    -pi*I*x\       
      |------- + --------| *\- e       + e       /       
      \   2         2    /
−π(ei(1−2x)+ei(2x−1))(eiπx+e−iπx)2(−eiπx+e−iπx)2(eiπx2+e−iπx2)2- \frac{\pi \left(e^{i \left(1 - 2 x\right)} + e^{i \left(2 x - 1\right)}\right) \left(e^{i \pi x} + e^{- i \pi x}\right)^{2}}{\left(- e^{i \pi x} + e^{- i \pi x}\right)^{2} \left(\frac{e^{i \pi x}}{2} + \frac{e^{- i \pi x}}{2}\right)^{2}} 
-pi*(exp(pi*i*x) + exp(-pi*i*x))^2*(exp(i*(1 - 2*x)) + exp(i*(-1 + 2*x)))/((exp(pi*i*x)/2 + exp(-pi*i*x)/2)^2*(-exp(pi*i*x) + exp(-pi*i*x))^2)
Unión de expresiones racionales [src] 
  2*pi*cos(-1 + 2*x) 
---------------------
   2          2      
cos (pi*x)*tan (pi*x)
2πcos⁡(2x−1)cos⁡2(πx)tan⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
2*pi*cos(-1 + 2*x)/(cos(pi*x)^2*tan(pi*x)^2)
Denominador racional [src] 
  2*pi*cos(-1 + 2*x) 
---------------------
   2          2      
cos (pi*x)*tan (pi*x)
2πcos⁡(2x−1)cos⁡2(πx)tan⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
2*pi*cos(-1 + 2*x)/(cos(pi*x)^2*tan(pi*x)^2)
Abrimos la expresión [src] 
                                   2                                       
       2*pi*cos(1)         4*pi*cos (x)*cos(1)    4*pi*cos(x)*sin(1)*sin(x)
- --------------------- + --------------------- + -------------------------
     2          2            2          2              2          2        
  cos (pi*x)*tan (pi*x)   cos (pi*x)*tan (pi*x)     cos (pi*x)*tan (pi*x)
4πsin⁡(1)sin⁡(x)cos⁡(x)cos⁡2(πx)tan⁡2(πx)+4πcos⁡(1)cos⁡2(x)cos⁡2(πx)tan⁡2(πx)−2πcos⁡(1)cos⁡2(πx)tan⁡2(πx)\frac{4 \pi \sin{\left(1 \right)} \sin{\left(x \right)} \cos{\left(x \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} + \frac{4 \pi \cos{\left(1 \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} - \frac{2 \pi \cos{\left(1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
  2*pi*cos(2*x - 1)  
---------------------
   2          2      
cos (pi*x)*tan (pi*x)
2πcos⁡(2x−1)cos⁡2(πx)tan⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
2*pi*cos(2*x - 1)/(cos(pi*x)^2*tan(pi*x)^2)
Compilar la expresión [src] 
  2*pi*cos(2*x - 1)  
---------------------
   2          2      
cos (pi*x)*tan (pi*x)
2πcos⁡(2x−1)cos⁡2(πx)tan⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x \right)} \tan^{2}{\left(\pi x \right)}} 
2*pi*cos(2*x - 1)/(cos(pi*x)^2*tan(pi*x)^2)
Parte trigonométrica [src] 
                  2    2       /       2          \
pi*(1 + cos(pi*x)) *csc (pi*x)*\1 - tan (-1/2 + x)/
---------------------------------------------------
           /       2          \    4/pi*x\         
         2*\1 + tan (-1/2 + x)/*cos |----|         
                                    \ 2  /
π(1−tan⁡2(x−12))(cos⁡(πx)+1)2csc⁡2(πx)2(tan⁡2(x−12)+1)cos⁡4(πx2)\frac{\pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right) \left(\cos{\left(\pi x \right)} + 1\right)^{2} \csc^{2}{\left(\pi x \right)}}{2 \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \cos^{4}{\left(\frac{\pi x}{2} \right)}} 
                              /         4          \              
                    2         |    4*sin (-1/2 + x)|              
              pi*sin (2*pi*x)*|1 - ----------------|              
                              |        2           |              
                              \     sin (-1 + 2*x) /              
------------------------------------------------------------------
                    2                                             
  /         4/pi*x\\                                              
  |    4*sin |----||  /         4          \                      
  |          \ 2  /|  |    4*sin (-1/2 + x)|    4/pi*x\    4      
2*|1 - ------------| *|1 + ----------------|*cos |----|*sin (pi*x)
  |        2       |  |        2           |     \ 2  /           
  \     sin (pi*x) /  \     sin (-1 + 2*x) /
π(−4sin⁡4(x−12)sin⁡2(2x−1)+1)sin⁡2(2πx)2(−4sin⁡4(πx2)sin⁡2(πx)+1)2(4sin⁡4(x−12)sin⁡2(2x−1)+1)sin⁡4(πx)cos⁡4(πx2)\frac{\pi \left(- \frac{4 \sin^{4}{\left(x - \frac{1}{2} \right)}}{\sin^{2}{\left(2 x - 1 \right)}} + 1\right) \sin^{2}{\left(2 \pi x \right)}}{2 \left(- \frac{4 \sin^{4}{\left(\frac{\pi x}{2} \right)}}{\sin^{2}{\left(\pi x \right)}} + 1\right)^{2} \left(\frac{4 \sin^{4}{\left(x - \frac{1}{2} \right)}}{\sin^{2}{\left(2 x - 1 \right)}} + 1\right) \sin^{4}{\left(\pi x \right)} \cos^{4}{\left(\frac{\pi x}{2} \right)}} 
        /     pi      \
4*pi*sin|-1 + -- + 2*x|
        \     2       /
-----------------------
         /pi         \ 
  1 - sin|-- + 2*pi*x| 
         \2          /
4πsin⁡(2x−1+π2)1−sin⁡(2πx+π2)\frac{4 \pi \sin{\left(2 x - 1 + \frac{\pi}{2} \right)}}{1 - \sin{\left(2 \pi x + \frac{\pi}{2} \right)}} 
             /       2          \           
          pi*\1 - tan (-1/2 + x)/           
--------------------------------------------
  /       2          \    4/pi*x\    2/pi*x\
2*\1 + tan (-1/2 + x)/*cos |----|*tan |----|
                           \ 2  /     \ 2  /
π(1−tan⁡2(x−12))2(tan⁡2(x−12)+1)cos⁡4(πx2)tan⁡2(πx2)\frac{\pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right)}{2 \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \cos^{4}{\left(\frac{\pi x}{2} \right)} \tan^{2}{\left(\frac{\pi x}{2} \right)}} 
                                 /         4          \                
                       2         |    4*sin (-1/2 + x)|                
                 pi*sin (2*pi*x)*|1 - ----------------|                
                                 |        2           |                
                                 \     sin (-1 + 2*x) /                
-----------------------------------------------------------------------
                    2                                                  
  /         4/pi*x\\                                                   
  |    4*sin |----||  /         4          \                           
  |          \ 2  /|  |    4*sin (-1/2 + x)|    4          4/pi   pi*x\
2*|1 - ------------| *|1 + ----------------|*sin (pi*x)*sin |-- + ----|
  |        2       |  |        2           |                \2     2  /
  \     sin (pi*x) /  \     sin (-1 + 2*x) /
π(−4sin⁡4(x−12)sin⁡2(2x−1)+1)sin⁡2(2πx)2(−4sin⁡4(πx2)sin⁡2(πx)+1)2(4sin⁡4(x−12)sin⁡2(2x−1)+1)sin⁡4(πx)sin⁡4(πx2+π2)\frac{\pi \left(- \frac{4 \sin^{4}{\left(x - \frac{1}{2} \right)}}{\sin^{2}{\left(2 x - 1 \right)}} + 1\right) \sin^{2}{\left(2 \pi x \right)}}{2 \left(- \frac{4 \sin^{4}{\left(\frac{\pi x}{2} \right)}}{\sin^{2}{\left(\pi x \right)}} + 1\right)^{2} \left(\frac{4 \sin^{4}{\left(x - \frac{1}{2} \right)}}{\sin^{2}{\left(2 x - 1 \right)}} + 1\right) \sin^{4}{\left(\pi x \right)} \sin^{4}{\left(\frac{\pi x}{2} + \frac{\pi}{2} \right)}} 
        2          2          4/pi*x\ /           1       \
2*pi*cos (pi*x)*csc (pi*x)*csc |----|*|-1 + --------------|
                               \ 2  / |        2          |
                                      \     tan (-1/2 + x)/
-----------------------------------------------------------
                              2                            
             /         1     \     2                       
             |-1 + ----------| *csc (-1/2 + x)             
             |        2/pi*x\|                             
             |     tan |----||                             
             \         \ 2  //
2π(−1+1tan⁡2(x−12))cos⁡2(πx)csc⁡4(πx2)csc⁡2(πx)(−1+1tan⁡2(πx2))2csc⁡2(x−12)\frac{2 \pi \left(-1 + \frac{1}{\tan^{2}{\left(x - \frac{1}{2} \right)}}\right) \cos^{2}{\left(\pi x \right)} \csc^{4}{\left(\frac{\pi x}{2} \right)} \csc^{2}{\left(\pi x \right)}}{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{\pi x}{2} \right)}}\right)^{2} \csc^{2}{\left(x - \frac{1}{2} \right)}} 
                                 4                                 
                 /       2/pi*x\\  /       2          \            
            2*pi*|1 + tan |----|| *\1 - tan (-1/2 + x)/            
                 \        \ 4  //                                  
-------------------------------------------------------------------
                                     2                 4           
/       2          \ /       2/pi*x\\  /       2/pi*x\\     2      
\1 + tan (-1/2 + x)/*|1 - tan |----|| *|1 - tan |----|| *tan (pi*x)
                     \        \ 2  //  \        \ 4  //
2π(1−tan⁡2(x−12))(tan⁡2(πx4)+1)4(1−tan⁡2(πx4))4(1−tan⁡2(πx2))2(tan⁡2(x−12)+1)tan⁡2(πx)\frac{2 \pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right) \left(\tan^{2}{\left(\frac{\pi x}{4} \right)} + 1\right)^{4}}{\left(1 - \tan^{2}{\left(\frac{\pi x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \tan^{2}{\left(\pi x \right)}} 
2*pi*cos(-1 + 2*x)
------------------
       2          
    sin (pi*x)
2πcos⁡(2x−1)sin⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\sin^{2}{\left(\pi x \right)}} 
4*pi*cos(-1 + 2*x)
------------------
 1 - cos(2*pi*x)
4πcos⁡(2x−1)1−cos⁡(2πx)\frac{4 \pi \cos{\left(2 x - 1 \right)}}{1 - \cos{\left(2 \pi x \right)}} 
      2          2/  1   x\    4/  1   x\    4/pi*x\ /        2          \
pi*cot (pi*x)*cot |- - + -|*sin |- - + -|*tan |----|*\-1 + cot (-1/2 + x)/
                  \  4   2/     \  4   2/     \ 4  /                      
--------------------------------------------------------------------------
                                        2                                 
                       /        2/pi*x\\     8/pi*x\                      
                     2*|-1 + cot |----|| *sin |----|                      
                       \         \ 2  //      \ 4  /
π(cot⁡2(x−12)−1)sin⁡4(x2−14)tan⁡4(πx4)cot⁡2(πx)cot⁡2(x2−14)2(cot⁡2(πx2)−1)2sin⁡8(πx4)\frac{\pi \left(\cot^{2}{\left(x - \frac{1}{2} \right)} - 1\right) \sin^{4}{\left(\frac{x}{2} - \frac{1}{4} \right)} \tan^{4}{\left(\frac{\pi x}{4} \right)} \cot^{2}{\left(\pi x \right)} \cot^{2}{\left(\frac{x}{2} - \frac{1}{4} \right)}}{2 \left(\cot^{2}{\left(\frac{\pi x}{2} \right)} - 1\right)^{2} \sin^{8}{\left(\frac{\pi x}{4} \right)}} 
                                   /         2            \ 
         4/pi*x\    2/  pi       \ |      sec (-1/2 + x)  | 
 2*pi*sec |----|*sec |- -- + pi*x|*|1 - ------------------| 
          \ 2  /     \  2        / |       2/  1       pi\| 
                                   |    sec |- - + x - --|| 
                                   \        \  2       2 // 
------------------------------------------------------------
                                                2           
                         /           2/pi*x\   \            
/         2            \ |        sec |----|   |            
|      sec (-1/2 + x)  | |            \ 2  /   |     2      
|1 + ------------------|*|1 - -----------------| *sec (pi*x)
|       2/  1       pi\| |       2/  pi   pi*x\|            
|    sec |- - + x - --|| |    sec |- -- + ----||            
\        \  2       2 // \        \  2     2  //
2π(−sec⁡2(x−12)sec⁡2(x−π2−12)+1)sec⁡4(πx2)sec⁡2(πx−π2)(−sec⁡2(πx2)sec⁡2(πx2−π2)+1)2(sec⁡2(x−12)sec⁡2(x−π2−12)+1)sec⁡2(πx)\frac{2 \pi \left(- \frac{\sec^{2}{\left(x - \frac{1}{2} \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} - \frac{1}{2} \right)}} + 1\right) \sec^{4}{\left(\frac{\pi x}{2} \right)} \sec^{2}{\left(\pi x - \frac{\pi}{2} \right)}}{\left(- \frac{\sec^{2}{\left(\frac{\pi x}{2} \right)}}{\sec^{2}{\left(\frac{\pi x}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \left(\frac{\sec^{2}{\left(x - \frac{1}{2} \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} - \frac{1}{2} \right)}} + 1\right) \sec^{2}{\left(\pi x \right)}} 
        /     pi      \
2*pi*sin|-1 + -- + 2*x|
        \     2       /
-----------------------
          2            
       sin (pi*x)
2πsin⁡(2x−1+π2)sin⁡2(πx)\frac{2 \pi \sin{\left(2 x - 1 + \frac{\pi}{2} \right)}}{\sin^{2}{\left(\pi x \right)}} 
        /       2          \   
   2*pi*\1 - tan (-1/2 + x)/   
-------------------------------
/       2          \    2      
\1 + tan (-1/2 + x)/*sin (pi*x)
2π(1−tan⁡2(x−12))(tan⁡2(x−12)+1)sin⁡2(πx)\frac{2 \pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right)}{\left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \sin^{2}{\left(\pi x \right)}} 
                     2                                 
     /       2/pi*x\\     2       /        2          \
2*pi*|1 + cot |----|| *cot (pi*x)*\-1 + cot (-1/2 + x)/
     \        \ 2  //                                  
-------------------------------------------------------
                                              2        
        /       2          \ /        2/pi*x\\         
        \1 + cot (-1/2 + x)/*|-1 + cot |----||         
                             \         \ 2  //
2π(cot⁡2(πx2)+1)2(cot⁡2(x−12)−1)cot⁡2(πx)(cot⁡2(πx2)−1)2(cot⁡2(x−12)+1)\frac{2 \pi \left(\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(x - \frac{1}{2} \right)} - 1\right) \cot^{2}{\left(\pi x \right)}}{\left(\cot^{2}{\left(\frac{\pi x}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(x - \frac{1}{2} \right)} + 1\right)} 
      2            /     pi      \
pi*sin (2*pi*x)*sin|-1 + -- + 2*x|
                   \     2       /
----------------------------------
        4          2/pi       \   
   2*sin (pi*x)*sin |-- + pi*x|   
                    \2        /
πsin⁡2(2πx)sin⁡(2x−1+π2)2sin⁡4(πx)sin⁡2(πx+π2)\frac{\pi \sin^{2}{\left(2 \pi x \right)} \sin{\left(2 x - 1 + \frac{\pi}{2} \right)}}{2 \sin^{4}{\left(\pi x \right)} \sin^{2}{\left(\pi x + \frac{\pi}{2} \right)}} 
                   2                     
   /       2/pi*x\\  /       2          \
pi*|1 + tan |----|| *\1 - tan (-1/2 + x)/
   \        \ 2  //                      
-----------------------------------------
      /       2          \    2/pi*x\    
    2*\1 + tan (-1/2 + x)/*tan |----|    
                               \ 2  /
π(1−tan⁡2(x−12))(tan⁡2(πx2)+1)22(tan⁡2(x−12)+1)tan⁡2(πx2)\frac{\pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right) \left(\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1\right)^{2}}{2 \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \tan^{2}{\left(\frac{\pi x}{2} \right)}} 
                   2    2           /           1       \
pi*(-1 + cos(pi*x)) *sin (-1/2 + x)*|-1 + --------------|
                                    |        2          |
                                    \     tan (-1/2 + x)/
---------------------------------------------------------
                      2          4/pi*x\                 
                 2*sin (pi*x)*sin |----|                 
                                  \ 2  /
π(−1+1tan⁡2(x−12))(cos⁡(πx)−1)2sin⁡2(x−12)2sin⁡4(πx2)sin⁡2(πx)\frac{\pi \left(-1 + \frac{1}{\tan^{2}{\left(x - \frac{1}{2} \right)}}\right) \left(\cos{\left(\pi x \right)} - 1\right)^{2} \sin^{2}{\left(x - \frac{1}{2} \right)}}{2 \sin^{4}{\left(\frac{\pi x}{2} \right)} \sin^{2}{\left(\pi x \right)}} 
                                   /       2/  1       pi\\                   
                                   |    cos |- - + x - --||                   
                           2       |        \  2       2 /|                   
                   2*pi*cos (pi*x)*|1 - ------------------|                   
                                   |         2            |                   
                                   \      cos (-1/2 + x)  /                   
------------------------------------------------------------------------------
                                                2                             
/       2/  1       pi\\ /       2/  pi   pi*x\\                              
|    cos |- - + x - --|| |    cos |- -- + ----||                              
|        \  2       2 /| |        \  2     2  /|     4/pi*x\    2/  pi       \
|1 + ------------------|*|1 - -----------------| *cos |----|*cos |- -- + pi*x|
|         2            | |           2/pi*x\   |      \ 2  /     \  2        /
\      cos (-1/2 + x)  / |        cos |----|   |                              
                         \            \ 2  /   /
2π(1−cos⁡2(x−π2−12)cos⁡2(x−12))cos⁡2(πx)(1−cos⁡2(πx2−π2)cos⁡2(πx2))2(1+cos⁡2(x−π2−12)cos⁡2(x−12))cos⁡4(πx2)cos⁡2(πx−π2)\frac{2 \pi \left(1 - \frac{\cos^{2}{\left(x - \frac{\pi}{2} - \frac{1}{2} \right)}}{\cos^{2}{\left(x - \frac{1}{2} \right)}}\right) \cos^{2}{\left(\pi x \right)}}{\left(1 - \frac{\cos^{2}{\left(\frac{\pi x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{\pi x}{2} \right)}}\right)^{2} \left(1 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} - \frac{1}{2} \right)}}{\cos^{2}{\left(x - \frac{1}{2} \right)}}\right) \cos^{4}{\left(\frac{\pi x}{2} \right)} \cos^{2}{\left(\pi x - \frac{\pi}{2} \right)}} 
                                    /       2/1   pi    \\   
                                    |    csc |- + -- - x||   
            2          4/pi   pi*x\ |        \2   2     /|   
    2*pi*csc (pi*x)*csc |-- - ----|*|1 - ----------------|   
                        \2     2  / |        2           |   
                                    \     csc (-1/2 + x) /   
-------------------------------------------------------------
                                            2                
/       2/1   pi    \\ /       2/pi   pi*x\\                 
|    csc |- + -- - x|| |    csc |-- - ----||                 
|        \2   2     /| |        \2     2  /|     2/pi       \
|1 + ----------------|*|1 - ---------------| *csc |-- - pi*x|
|        2           | |          2/pi*x\  |      \2        /
\     csc (-1/2 + x) / |       csc |----|  |                 
                       \           \ 2  /  /
2π(1−csc⁡2(−x+12+π2)csc⁡2(x−12))csc⁡2(πx)csc⁡4(−πx2+π2)(1−csc⁡2(−πx2+π2)csc⁡2(πx2))2(1+csc⁡2(−x+12+π2)csc⁡2(x−12))csc⁡2(−πx+π2)\frac{2 \pi \left(1 - \frac{\csc^{2}{\left(- x + \frac{1}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x - \frac{1}{2} \right)}}\right) \csc^{2}{\left(\pi x \right)} \csc^{4}{\left(- \frac{\pi x}{2} + \frac{\pi}{2} \right)}}{\left(1 - \frac{\csc^{2}{\left(- \frac{\pi x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{\pi x}{2} \right)}}\right)^{2} \left(1 + \frac{\csc^{2}{\left(- x + \frac{1}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x - \frac{1}{2} \right)}}\right) \csc^{2}{\left(- \pi x + \frac{\pi}{2} \right)}} 
        2                    
2*pi*csc (pi*x)*cos(-1 + 2*x)
2πcos⁡(2x−1)csc⁡2(πx)2 \pi \cos{\left(2 x - 1 \right)} \csc^{2}{\left(\pi x \right)} 
2*pi*cos(2*x - 1)
-----------------
       2         
    sin (pi*x)
2πcos⁡(2x−1)sin⁡2(πx)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\sin^{2}{\left(\pi x \right)}} 
                  4*pi                  
----------------------------------------
/           1        \    /    pi      \
|1 - ----------------|*csc|1 + -- - 2*x|
|       /pi         \|    \    2       /
|    csc|-- - 2*pi*x||                  
\       \2          //
4π(1−1csc⁡(−2πx+π2))csc⁡(−2x+1+π2)\frac{4 \pi}{\left(1 - \frac{1}{\csc{\left(- 2 \pi x + \frac{\pi}{2} \right)}}\right) \csc{\left(- 2 x + 1 + \frac{\pi}{2} \right)}} 
                             /         2           \  
          2          4/pi*x\ |      csc (-1/2 + x) |  
  2*pi*csc (pi*x)*csc |----|*|-1 + ----------------|  
                      \ 2  / |        2/1   pi    \|  
                             |     csc |- + -- - x||  
                             \         \2   2     //  
------------------------------------------------------
                      2                               
/           2/pi*x\  \                                
|        csc |----|  |                                
|            \ 2  /  |     2              2/pi       \
|-1 + ---------------| *csc (-1/2 + x)*csc |-- - pi*x|
|        2/pi   pi*x\|                     \2        /
|     csc |-- - ----||                                
\         \2     2  //
2π(csc⁡2(x−12)csc⁡2(−x+12+π2)−1)csc⁡4(πx2)csc⁡2(πx)(csc⁡2(πx2)csc⁡2(−πx2+π2)−1)2csc⁡2(x−12)csc⁡2(−πx+π2)\frac{2 \pi \left(\frac{\csc^{2}{\left(x - \frac{1}{2} \right)}}{\csc^{2}{\left(- x + \frac{1}{2} + \frac{\pi}{2} \right)}} - 1\right) \csc^{4}{\left(\frac{\pi x}{2} \right)} \csc^{2}{\left(\pi x \right)}}{\left(\frac{\csc^{2}{\left(\frac{\pi x}{2} \right)}}{\csc^{2}{\left(- \frac{\pi x}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2} \csc^{2}{\left(x - \frac{1}{2} \right)} \csc^{2}{\left(- \pi x + \frac{\pi}{2} \right)}} 
        2/  pi       \
2*pi*sec |- -- + pi*x|
         \  2        /
----------------------
    sec(-1 + 2*x)
2πsec⁡2(πx−π2)sec⁡(2x−1)\frac{2 \pi \sec^{2}{\left(\pi x - \frac{\pi}{2} \right)}}{\sec{\left(2 x - 1 \right)}} 
                    2 /       2          \  
  pi*(1 + cos(pi*x)) *\1 - tan (-1/2 + x)/  
--------------------------------------------
  /       2          \    4/pi*x\    2      
2*\1 + tan (-1/2 + x)/*cos |----|*sin (pi*x)
                           \ 2  /
π(1−tan⁡2(x−12))(cos⁡(πx)+1)22(tan⁡2(x−12)+1)sin⁡2(πx)cos⁡4(πx2)\frac{\pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right) \left(\cos{\left(\pi x \right)} + 1\right)^{2}}{2 \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \sin^{2}{\left(\pi x \right)} \cos^{4}{\left(\frac{\pi x}{2} \right)}} 
                       4                                       
       /       2/pi*x\\     2/  1   x\ /           1       \   
    pi*|1 + tan |----|| *tan |- - + -|*|-1 + --------------|   
       \        \ 4  //      \  4   2/ |        2          |   
                                       \     tan (-1/2 + x)/   
---------------------------------------------------------------
                     2                  2                      
  /       2/  1   x\\  /         1     \     2          4/pi*x\
2*|1 + tan |- - + -|| *|-1 + ----------| *tan (pi*x)*tan |----|
  \        \  4   2//  |        2/pi*x\|                 \ 4  /
                       |     tan |----||                       
                       \         \ 2  //
π(−1+1tan⁡2(x−12))(tan⁡2(πx4)+1)4tan⁡2(x2−14)2(−1+1tan⁡2(πx2))2(tan⁡2(x2−14)+1)2tan⁡4(πx4)tan⁡2(πx)\frac{\pi \left(-1 + \frac{1}{\tan^{2}{\left(x - \frac{1}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{\pi x}{4} \right)} + 1\right)^{4} \tan^{2}{\left(\frac{x}{2} - \frac{1}{4} \right)}}{2 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{\pi x}{2} \right)}}\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} - \frac{1}{4} \right)} + 1\right)^{2} \tan^{4}{\left(\frac{\pi x}{4} \right)} \tan^{2}{\left(\pi x \right)}} 
         2          4/pi*x\ /       2          \ 
 2*pi*cos (pi*x)*sec |----|*\1 - tan (-1/2 + x)/ 
                     \ 2  /                      
-------------------------------------------------
                                     2           
/       2          \ /       2/pi*x\\     2      
\1 + tan (-1/2 + x)/*|1 - tan |----|| *sin (pi*x)
                     \        \ 2  //
2π(1−tan⁡2(x−12))cos⁡2(πx)sec⁡4(πx2)(1−tan⁡2(πx2))2(tan⁡2(x−12)+1)sin⁡2(πx)\frac{2 \pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right) \cos^{2}{\left(\pi x \right)} \sec^{4}{\left(\frac{\pi x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \sin^{2}{\left(\pi x \right)}} 
                                         /        2/  1       pi\\
                                         |     sec |- - + x - --||
        2/  pi       \    4/  pi   pi*x\ |         \  2       2 /|
2*pi*sec |- -- + pi*x|*sec |- -- + ----|*|-1 + ------------------|
         \  2        /     \  2     2  / |          2            |
                                         \       sec (-1/2 + x)  /
------------------------------------------------------------------
                             2                                    
     /        2/  pi   pi*x\\                                     
     |     sec |- -- + ----||                                     
     |         \  2     2  /|     2          2/  1       pi\      
     |-1 + -----------------| *sec (pi*x)*sec |- - + x - --|      
     |            2/pi*x\   |                 \  2       2 /      
     |         sec |----|   |                                     
     \             \ 2  /   /
2π(−1+sec⁡2(x−π2−12)sec⁡2(x−12))sec⁡4(πx2−π2)sec⁡2(πx−π2)(−1+sec⁡2(πx2−π2)sec⁡2(πx2))2sec⁡2(πx)sec⁡2(x−π2−12)\frac{2 \pi \left(-1 + \frac{\sec^{2}{\left(x - \frac{\pi}{2} - \frac{1}{2} \right)}}{\sec^{2}{\left(x - \frac{1}{2} \right)}}\right) \sec^{4}{\left(\frac{\pi x}{2} - \frac{\pi}{2} \right)} \sec^{2}{\left(\pi x - \frac{\pi}{2} \right)}}{\left(-1 + \frac{\sec^{2}{\left(\frac{\pi x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{\pi x}{2} \right)}}\right)^{2} \sec^{2}{\left(\pi x \right)} \sec^{2}{\left(x - \frac{\pi}{2} - \frac{1}{2} \right)}} 
         2       
 2*pi*csc (pi*x) 
-----------------
   /    pi      \
csc|1 + -- - 2*x|
   \    2       /
2πcsc⁡2(πx)csc⁡(−2x+1+π2)\frac{2 \pi \csc^{2}{\left(\pi x \right)}}{\csc{\left(- 2 x + 1 + \frac{\pi}{2} \right)}} 
        2/pi       \
2*pi*sec |-- - pi*x|
         \2        /
--------------------
   sec(-1 + 2*x)
2πsec⁡2(−πx+π2)sec⁡(2x−1)\frac{2 \pi \sec^{2}{\left(- \pi x + \frac{\pi}{2} \right)}}{\sec{\left(2 x - 1 \right)}} 
             /        2          \        
        4*pi*\-1 + cot (-1/2 + x)/        
------------------------------------------
                     /            2      \
/       2          \ |    -1 + cot (pi*x)|
\1 + cot (-1/2 + x)/*|1 - ---------------|
                     |            2      |
                     \     1 + cot (pi*x)/
4π(cot⁡2(x−12)−1)(−cot⁡2(πx)−1cot⁡2(πx)+1+1)(cot⁡2(x−12)+1)\frac{4 \pi \left(\cot^{2}{\left(x - \frac{1}{2} \right)} - 1\right)}{\left(- \frac{\cot^{2}{\left(\pi x \right)} - 1}{\cot^{2}{\left(\pi x \right)} + 1} + 1\right) \left(\cot^{2}{\left(x - \frac{1}{2} \right)} + 1\right)} 
              4*pi             
-------------------------------
/         1     \              
|1 - -----------|*sec(-1 + 2*x)
\    sec(2*pi*x)/
4π(1−1sec⁡(2πx))sec⁡(2x−1)\frac{4 \pi}{\left(1 - \frac{1}{\sec{\left(2 \pi x \right)}}\right) \sec{\left(2 x - 1 \right)}} 
                   4                                               
   /       2/pi*x\\     2          2/  1   x\ /        2          \
pi*|1 + cot |----|| *cot (pi*x)*cot |- - + -|*\-1 + cot (-1/2 + x)/
   \        \ 4  //                 \  4   2/                      
-------------------------------------------------------------------
                             2                  2                  
          /       2/  1   x\\  /        2/pi*x\\     4/pi*x\       
        2*|1 + cot |- - + -|| *|-1 + cot |----|| *cot |----|       
          \        \  4   2//  \         \ 2  //      \ 4  /
π(cot⁡2(πx4)+1)4(cot⁡2(x−12)−1)cot⁡2(πx)cot⁡2(x2−14)2(cot⁡2(πx2)−1)2(cot⁡2(x2−14)+1)2cot⁡4(πx4)\frac{\pi \left(\cot^{2}{\left(\frac{\pi x}{4} \right)} + 1\right)^{4} \left(\cot^{2}{\left(x - \frac{1}{2} \right)} - 1\right) \cot^{2}{\left(\pi x \right)} \cot^{2}{\left(\frac{x}{2} - \frac{1}{4} \right)}}{2 \left(\cot^{2}{\left(\frac{\pi x}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} - \frac{1}{4} \right)} + 1\right)^{2} \cot^{4}{\left(\frac{\pi x}{4} \right)}} 
        2          2           /        2          \
2*pi*cot (pi*x)*sin (-1/2 + x)*\-1 + cot (-1/2 + x)/
----------------------------------------------------
                            2                       
           /        2/pi*x\\     4/pi*x\            
           |-1 + cot |----|| *sin |----|            
           \         \ 2  //      \ 2  /
2π(cot⁡2(x−12)−1)sin⁡2(x−12)cot⁡2(πx)(cot⁡2(πx2)−1)2sin⁡4(πx2)\frac{2 \pi \left(\cot^{2}{\left(x - \frac{1}{2} \right)} - 1\right) \sin^{2}{\left(x - \frac{1}{2} \right)} \cot^{2}{\left(\pi x \right)}}{\left(\cot^{2}{\left(\frac{\pi x}{2} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{\pi x}{2} \right)}} 
                       4                                 
       /       2/pi*x\\     2       /          1       \ 
  2*pi*|1 + cot |----|| *cot (pi*x)*|1 - --------------| 
       \        \ 4  //             |       2          | 
                                    \    cot (-1/2 + x)/ 
---------------------------------------------------------
                                     2                  4
/          1       \ /        1     \  /        2/pi*x\\ 
|1 + --------------|*|1 - ----------| *|-1 + cot |----|| 
|       2          | |       2/pi*x\|  \         \ 4  // 
\    cot (-1/2 + x)/ |    cot |----||                    
                     \        \ 2  //
2π(1−1cot⁡2(x−12))(cot⁡2(πx4)+1)4cot⁡2(πx)(1−1cot⁡2(πx2))2(1+1cot⁡2(x−12))(cot⁡2(πx4)−1)4\frac{2 \pi \left(1 - \frac{1}{\cot^{2}{\left(x - \frac{1}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{\pi x}{4} \right)} + 1\right)^{4} \cot^{2}{\left(\pi x \right)}}{\left(1 - \frac{1}{\cot^{2}{\left(\frac{\pi x}{2} \right)}}\right)^{2} \left(1 + \frac{1}{\cot^{2}{\left(x - \frac{1}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{\pi x}{4} \right)} - 1\right)^{4}} 
                        2       /       2          \                
                2*pi*cot (pi*x)*\1 - tan (-1/2 + x)/                
--------------------------------------------------------------------
                                     2                  4           
/       2          \ /       2/pi*x\\  /        2/pi*x\\     8/pi*x\
\1 + tan (-1/2 + x)/*|1 - tan |----|| *|-1 + cot |----|| *sin |----|
                     \        \ 2  //  \         \ 4  //      \ 4  /
2π(1−tan⁡2(x−12))cot⁡2(πx)(1−tan⁡2(πx2))2(tan⁡2(x−12)+1)(cot⁡2(πx4)−1)4sin⁡8(πx4)\frac{2 \pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right) \cot^{2}{\left(\pi x \right)}}{\left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi x}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{\pi x}{4} \right)}} 
                               /       2          \                           
                          2*pi*\1 - tan (-1/2 + x)/                           
------------------------------------------------------------------------------
                                     2                 4                      
/       2          \ /       2/pi*x\\  /       2/pi*x\\     8/pi*x\    2      
\1 + tan (-1/2 + x)/*|1 - tan |----|| *|1 - tan |----|| *cos |----|*tan (pi*x)
                     \        \ 2  //  \        \ 4  //      \ 4  /
2π(1−tan⁡2(x−12))(1−tan⁡2(πx4))4(1−tan⁡2(πx2))2(tan⁡2(x−12)+1)cos⁡8(πx4)tan⁡2(πx)\frac{2 \pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right)}{\left(1 - \tan^{2}{\left(\frac{\pi x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \cos^{8}{\left(\frac{\pi x}{4} \right)} \tan^{2}{\left(\pi x \right)}} 
        2      
2*pi*csc (pi*x)
---------------
 sec(-1 + 2*x)
2πcsc⁡2(πx)sec⁡(2x−1)\frac{2 \pi \csc^{2}{\left(\pi x \right)}}{\sec{\left(2 x - 1 \right)}} 
      2                      
pi*sin (2*pi*x)*cos(-1 + 2*x)
-----------------------------
        2          4         
   2*cos (pi*x)*sin (pi*x)
πsin⁡2(2πx)cos⁡(2x−1)2sin⁡4(πx)cos⁡2(πx)\frac{\pi \sin^{2}{\left(2 \pi x \right)} \cos{\left(2 x - 1 \right)}}{2 \sin^{4}{\left(\pi x \right)} \cos^{2}{\left(\pi x \right)}} 
                   2                      
   /       2/pi*x\\  /        2          \
pi*|1 + cot |----|| *\-1 + cot (-1/2 + x)/
   \        \ 2  //                       
------------------------------------------
      /       2          \    2/pi*x\     
    2*\1 + cot (-1/2 + x)/*cot |----|     
                               \ 2  /
π(cot⁡2(πx2)+1)2(cot⁡2(x−12)−1)2(cot⁡2(x−12)+1)cot⁡2(πx2)\frac{\pi \left(\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(x - \frac{1}{2} \right)} - 1\right)}{2 \left(\cot^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \cot^{2}{\left(\frac{\pi x}{2} \right)}} 
             /       2          \        
        4*pi*\1 - tan (-1/2 + x)/        
-----------------------------------------
                     /           2      \
/       2          \ |    1 - tan (pi*x)|
\1 + tan (-1/2 + x)/*|1 - --------------|
                     |           2      |
                     \    1 + tan (pi*x)/
4π(1−tan⁡2(x−12))(−1−tan⁡2(πx)tan⁡2(πx)+1+1)(tan⁡2(x−12)+1)\frac{4 \pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right)}{\left(- \frac{1 - \tan^{2}{\left(\pi x \right)}}{\tan^{2}{\left(\pi x \right)} + 1} + 1\right) \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right)} 
                                    /          2            \
         2          2/  1       pi\ |       cos (-1/2 + x)  |
 2*pi*cos (pi*x)*cos |- - + x - --|*|-1 + ------------------|
                     \  2       2 / |        2/  1       pi\|
                                    |     cos |- - + x - --||
                                    \         \  2       2 //
-------------------------------------------------------------
                        2                                    
/            2/pi*x\   \                                     
|         cos |----|   |                                     
|             \ 2  /   |     2/  pi       \    4/  pi   pi*x\
|-1 + -----------------| *cos |- -- + pi*x|*cos |- -- + ----|
|        2/  pi   pi*x\|      \  2        /     \  2     2  /
|     cos |- -- + ----||                                     
\         \  2     2  //
2π(cos⁡2(x−12)cos⁡2(x−π2−12)−1)cos⁡2(πx)cos⁡2(x−π2−12)(cos⁡2(πx2)cos⁡2(πx2−π2)−1)2cos⁡4(πx2−π2)cos⁡2(πx−π2)\frac{2 \pi \left(\frac{\cos^{2}{\left(x - \frac{1}{2} \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} - \frac{1}{2} \right)}} - 1\right) \cos^{2}{\left(\pi x \right)} \cos^{2}{\left(x - \frac{\pi}{2} - \frac{1}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{\pi x}{2} \right)}}{\cos^{2}{\left(\frac{\pi x}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2} \cos^{4}{\left(\frac{\pi x}{2} - \frac{\pi}{2} \right)} \cos^{2}{\left(\pi x - \frac{\pi}{2} \right)}} 
2*pi*cos(-1 + 2*x)
------------------
   2/  pi       \ 
cos |- -- + pi*x| 
    \  2        /
2πcos⁡(2x−1)cos⁡2(πx−π2)\frac{2 \pi \cos{\left(2 x - 1 \right)}}{\cos^{2}{\left(\pi x - \frac{\pi}{2} \right)}} 
                               /         2           \
      2            2           |      sin (-1 + 2*x) |
pi*sin (2*pi*x)*sin (-1/2 + x)*|-1 + ----------------|
                               |          4          |
                               \     4*sin (-1/2 + x)/
------------------------------------------------------
                          2                           
       /         2       \                            
       |      sin (pi*x) |     4          4/pi*x\     
     2*|-1 + ------------| *sin (pi*x)*sin |----|     
       |          4/pi*x\|                 \ 2  /     
       |     4*sin |----||                            
       \           \ 2  //
π(−1+sin⁡2(2x−1)4sin⁡4(x−12))sin⁡2(2πx)sin⁡2(x−12)2(−1+sin⁡2(πx)4sin⁡4(πx2))2sin⁡4(πx2)sin⁡4(πx)\frac{\pi \left(-1 + \frac{\sin^{2}{\left(2 x - 1 \right)}}{4 \sin^{4}{\left(x - \frac{1}{2} \right)}}\right) \sin^{2}{\left(2 \pi x \right)} \sin^{2}{\left(x - \frac{1}{2} \right)}}{2 \left(-1 + \frac{\sin^{2}{\left(\pi x \right)}}{4 \sin^{4}{\left(\frac{\pi x}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{\pi x}{2} \right)} \sin^{4}{\left(\pi x \right)}} 
                        2                        
        /       2/pi*x\\  /       2          \   
   2*pi*|1 + tan |----|| *\1 - tan (-1/2 + x)/   
        \        \ 2  //                         
-------------------------------------------------
                                     2           
/       2          \ /       2/pi*x\\     2      
\1 + tan (-1/2 + x)/*|1 - tan |----|| *tan (pi*x)
                     \        \ 2  //
2π(1−tan⁡2(x−12))(tan⁡2(πx2)+1)2(1−tan⁡2(πx2))2(tan⁡2(x−12)+1)tan⁡2(πx)\frac{2 \pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right) \left(\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \tan^{2}{\left(\pi x \right)}} 
                        2/  1   x\ /           1       \                  
                  pi*tan |- - + -|*|-1 + --------------|                  
                         \  4   2/ |        2          |                  
                                   \     tan (-1/2 + x)/                  
--------------------------------------------------------------------------
                     2                  2                                 
  /       2/  1   x\\  /         1     \     8/pi*x\    2          4/pi*x\
2*|1 + tan |- - + -|| *|-1 + ----------| *cos |----|*tan (pi*x)*tan |----|
  \        \  4   2//  |        2/pi*x\|      \ 4  /                \ 4  /
                       |     tan |----||                                  
                       \         \ 2  //
π(−1+1tan⁡2(x−12))tan⁡2(x2−14)2(−1+1tan⁡2(πx2))2(tan⁡2(x2−14)+1)2cos⁡8(πx4)tan⁡4(πx4)tan⁡2(πx)\frac{\pi \left(-1 + \frac{1}{\tan^{2}{\left(x - \frac{1}{2} \right)}}\right) \tan^{2}{\left(\frac{x}{2} - \frac{1}{4} \right)}}{2 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{\pi x}{2} \right)}}\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} - \frac{1}{4} \right)} + 1\right)^{2} \cos^{8}{\left(\frac{\pi x}{4} \right)} \tan^{4}{\left(\frac{\pi x}{4} \right)} \tan^{2}{\left(\pi x \right)}} 
                      /       2          \                  
                 2*pi*\1 - tan (-1/2 + x)/                  
------------------------------------------------------------
                                     2                      
/       2          \ /       2/pi*x\\     4/pi*x\    2      
\1 + tan (-1/2 + x)/*|1 - tan |----|| *cos |----|*tan (pi*x)
                     \        \ 2  //      \ 2  /
2π(1−tan⁡2(x−12))(1−tan⁡2(πx2))2(tan⁡2(x−12)+1)cos⁡4(πx2)tan⁡2(πx)\frac{2 \pi \left(1 - \tan^{2}{\left(x - \frac{1}{2} \right)}\right)}{\left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(x - \frac{1}{2} \right)} + 1\right) \cos^{4}{\left(\frac{\pi x}{2} \right)} \tan^{2}{\left(\pi x \right)}} 
2*pi*(1 - tan(-1/2 + x)^2)/((1 + tan(-1/2 + x)^2)*(1 - tan(pi*x/2)^2)^2*cos(pi*x/2)^4*tan(pi*x)^2)
    © Sr Examen – Калькулятор